CN103413016B - A kind of aircaft configuration safe life based on test and use data fusion of being on active service determines method - Google Patents

Abstract

The invention discloses a kind of aircaft configuration safe life based on test and use data fusion of being on active service and determine that method, summary of the invention include that when homotype aircraft different loads spectrum lower test data fatigue life and use data fatigue life of being on active service obey logarithm normal distribution, group of planes safe life determines that method and the homotype aircraft group of planes safe life under same test load is composed determines method.When homotype aircraft different loads spectrum lower test data fatigue life and use data fatigue life of being on active service obey logarithm normal distribution, group of planes safe life determines that method comprises the following steps: obtain aircaft configuration random censorship data fatigue life；Calculate aircraft structure fatigue life distribution function parameter；Calculate armada Fatigue Life Scatter Factor's and safe life.Homotype aircraft group of planes safe life under same test load is composed determines that method comprises the following steps: calculate military service CALCULATING STRUCTURAL FATIGUE DAMAGE OF AIRCRAFT value and equivalent pilot time or the number of times that rises and falls；Obtain aircaft configuration random censorship data fatigue life；Calculate aircraft structure fatigue life distribution function parameter；Calculate the armada fatigue coefficient of dispersion and safe life.

Description

A kind of aircaft configuration safe life based on test and use data fusion of being on active service determines Method

Technical field

The invention belongs to aircaft configuration safe life computing technique field, particularly relate to a kind of based on testing and be on active service use The aircaft configuration safe life of data fusion determines method.

Background technology

The aircraft structure fatigue life-span is reflection aircaft configuration economy and the key parameter of safety, it with structural quality and Use condition is relevant.Due to the impact of uncertain factor, for ensureing the use safety of aircaft configuration, Aircraft Structural Life need to be carried out Fail-safe analysis.As determined by safe-life design criterion, aircaft configuration is referred to as safe life service life, and aircaft configuration is pacified Life-cycle N_{ρ, γ}Median fatigue life N for aircaft configuration₅₀With the tired coefficient of dispersion (that is Fatigue Life Scatter Factor's) L_fRatio Value, it may be assumed that

$N_{p,\mathrm{\γ}}=\frac{N_{50}}{L_f}$

Determine that the core of aircaft configuration safe life is FATIGUE LIFE DISTRIBUTION characteristic and the tired coefficient of dispersion.Visible fatigue is divided Scattered coefficient is a significant reliability index in Aircraft life evaluation work.For aircaft configuration, it is generally recognized that same The test load spectrum lower homotype aircraft structure fatigue life-span obeys logarithm normal distribution, and the determination method about the tired coefficient of dispersion is ground Study carefully and be also based on what logarithm normal distribution hypothesis obtained.The tired coefficient of dispersion computing formula that China uses is:

$L_f={10}^{\mathrm{\σ}(u_p+\frac{u_{\mathrm{\γ}}}{\sqrt{n}})}$

The reliability index that this formula is corresponding is survival rate p, confidence level γ, and test specimen number is n.Visible, for tired The labor coefficient of dispersion is sometimes it is contemplated that the impact of test specimen number size.

Aircaft configuration safe life is to use full machine fatigue test results to estimate the median fatigue life [N obtained₅₀] divided by Tired coefficient of dispersion L_fObtain.And China's full machine fatigue test (endurancing) is typically to randomly select 1 airplane and has come Become, say, that test specimen number is 1.After but aircraft sizing is delivered for use, is on active service and uses number of aircraft many, and it is believed that clothes The aircraft used also is to be on active service in reality to use the fatigue life test aircraft under environment.During aircraft is on active service, clothes Labour certain period of time after aircraft is carried out maintenance and inspection, can obtain aircaft configuration actual military service use pilot time number or Rise and fall number of times.For checking that the aircaft configuration finding to have lost efficacy just obtains test data of dying of old age, the aircraft for no-failure is tied Structure just obtains no-failure right truncation data of fatigue life.If former for aircaft configuration test data fatigue life are tieed up with checking The military service obtained when repairing uses random censorship data fatigue life to carry out merging for aircraft structural reliability analysis and assessment, then Sample size will be significantly increased, thus improve the accuracy of Reliability Analysis of Aircraft Structure.

Affect a lot of because have of aircraft structure fatigue life dispersivity, can be generally divided into two classes: inherent dispersibility and External dispersibility.Wherein inherent dispersibility refer to due to material, process, assembling etc. causes only relevant with architectural characteristic point Dissipate property, referred to as structure disperses；The dispersibility that external dispersibility refers to load-up condition and changes in environmental conditions and causes, and The dispersibility that environmental condition causes is smaller, so external dispersibility is commonly referred to as the dispersibility that load-up condition causes. Both dispersing characteristics all can use random variable of continuous type to describe, and it is generally acknowledged separate.

In the case of the impact not considering environment dispersibility, it is generally recognized that homotype aircraft structure fatigue under same loading spectrum Life-span obeys logarithm normal distribution.If homotype aircaft configuration causes aircaft configuration due to the difference of group of planes military service maneuvering load Also obey logarithm normal distribution fatigue life, then consider structure disperses and load scatter and the group of planes aircraft that causes is tired The labor life-span also can describe by logarithm normal distribution.Now, for the safe life analysis of group of planes aircraft, the random right of military service aircraft Truncation data fatigue life directly can merge for carrying out statistical analysis with flight test vehicle test data fatigue life With calculating.

Under same test load is composed, the homotype aircraft structure fatigue life-span obeys under logarithm normal distribution, if homotype aircraft Structure causes the aircraft structure fatigue life-span to disobey logarithm normal distribution, the most comprehensively due to the difference of group of planes military service maneuvering load The group of planes aircraft fatigue life-span considering structure disperses and load scatter and cause can not describe by logarithm normal distribution.This Time, homotype group of planes military service aircraft and flight test vehicle are to work in different usings method and under the conditions of using, flight test vehicle with Military service aircraft belongs to different parents, and their data fatigue life can not directly merge divides for carrying out aircraft structural reliability Analysis.And with experimental enviroment get off the plane test life result come analyses and prediction actual be on active service use environment get off the plane structure be on active service the longevity Life result has bigger error, how to make them belong to same parent, utilizes the military service of military service aircraft to use data to fly with test The safe life of machine test data computational analysis aircaft configuration, is one and becomes parent problem analysis.Therefore, it is necessary to find in one The area of a room, can change into the data under the same terms their data, thus it is believed that homotype takes after processing Labour aircraft and flight test vehicle are from same parent, thus carry out aircaft configuration safe life analytical calculation.Here can will take The load environment of labour aircraft uses the method for EQUIVALENT DAMAGE CONVERSION to be equivalent to flight test vehicle load environment and processes, flight test vehicle and clothes Labour aircraft is then from same parent, and fatigue life obeyed same logarithm with the right truncation of military service aircraft equivalent fatigue life by flight test vehicle Normal distribution.

Certainly, homotype armada after considering structure disperses and load scatter is still obeyed fatigue life right The situation of number normal distribution, for improving the accuracy of group of planes Reliability Analysis of Aircraft Structure, it would however also be possible to employ by military service aircraft Load environment EQUIVALENT DAMAGE CONVERSION is equivalent to the method for flight test vehicle load environment process and carries out aircaft configuration safe life analysis Calculate.Now, aircraft structure fatigue life standard error is just tied by the aircraft after considering structure disperses and load scatter Structure standard deviation fatigue life becomes only considering the aircraft structure fatigue life standard error of structure disperses.Generally, comprehensively Consider the aircraft structure fatigue life standard error after structure disperses and load scatter more than only considering flying of structure disperses Machine structure fatigue life standard deviation.

Summary of the invention

The purpose of the embodiment of the present invention is to provide a kind of aircaft configuration based on test and use data fusion of being on active service to pacify Life-cycle determines method, it is intended to solve the problem that during existing aircraft safety Life Calculation is analyzed, sample size is on the low side, and raising flies The accuracy of machine Analysis of structural reliability.

The embodiment of the present invention is achieved in that a kind of aircaft configuration safety using data fusion based on test and military service Life-span determines that method, described aircaft configuration safe life based on test and use data fusion of being on active service determine that method includes homotype Group of planes when aircraft different loads spectrum lower test data fatigue life and use data fatigue life of being on active service obey logarithm normal distribution Safe life determines method, and step is:

Step 1, obtains aircaft configuration random censorship data fatigue life: test fatigue under homotype aircraft different loads spectrum When lifetime data and use data fatigue life of being on active service obey logarithm normal distribution, it is believed that consider structure and loading spectrum dispersion Property and aircraft structure fatigue life-span of causing also describes by logarithm normal distribution, so tired with the lower flight test vehicle of different loads spectrum Lifetime data uses aircraft fatigue lifetime data to directly obtain aircaft configuration random censorship fatigue life after taking the logarithm with being on active service Data；

Step 2, calculating aircraft structure fatigue life distribution function parameter: the logarithm normal distribution under random censorship situation Likelihood function and the Maximum-likelihood estimation of lognormal distribution parameter；

Logarithm normal distribution likelihood function under described random censorship situation calculates and concretely comprises the following steps:

If the distribution function of life-span X is F (x, θ) (θ ∈ Θ), density function be f (x, θ), Θ be the non-NULL opener in R, From the parent that distribution function is F (x, θ), randomly draw n individuality, carry out life test；For each individuality, observe the life-span It is X_i(i=1 ..., n), correspondingly there is individual truncated time Y_i(i=1 ..., n), observation X that i-th individuality is obtained_i∧Y_i Take minima, make t_i=X_i∧Y_i,So can be obtained by data (t_i, δ_i) (i=1 ..., n), δ_i=1 Represent t_iIt is test failure data, δ_i=0 represents t_iIt it is non-failure data；Then data (t₁, δ₁) ..., (t_n, δ_n) likelihood function For:

$L\left(\mathrm{\θ}\right)=\underset{i=1}{\overset{n}{\mathrm{\Π}}}f{(t_i,\mathrm{\θ})}^{{\mathrm{\δ}}_i}{\[1-F(t_i,\mathrm{\θ})\]}^{1-{\mathrm{\δ}}_i}$

If N fatigue life of aircraft obeys logarithm normal distribution, then can be designated as

LgN=X～N (μ, σ²)

Distribution function and density function are respectively as follows:

$F\left(x\right)={\∫}_0^x\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}{e}^{-\frac{{(t-u)}^2}{2{\mathrm{\σ}}^2}}dt$

$f\left(x\right)=\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}{e}^{-\frac{{(x-\mathrm{\μ})}^2}{2{\mathrm{\σ}}^2}}$

X_i(i=1 ..., r) it is fatigue failure life, X_i(i=r+1 ..., n) it is the tired no-failure life-span；Then likelihood function For:

$L\left(\mathrm{\θ}\right)=\underset{i=1}{\overset{n}{\mathrm{\Π}}}f{(t_i,\mathrm{\θ})}^{{\mathrm{\δ}}_i}{\[1-F(t_i,\mathrm{\θ})\]}^{1-{\mathrm{\δ}}_i}$

$=\frac{1}{{\left(\sqrt{2\mathrm{\π}}\mathrm{\σ}\right)}^r}{e}^{-\underset{i=1}{\overset{r}{\mathrm{\Σ}}}\frac{{(x_i-\mathrm{\μ})}^2}{2{\mathrm{\σ}}^2}}\underset{i=r+1}{\overset{n}{\mathrm{\Π}}}\[{\∫}_{x_i}^{\mathrm{\∞}}\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}{e}^{-\frac{1}{2}{\left(\frac{t-\mathrm{\μ}}{\mathrm{\σ}}\right)}^2}dt\];$

Step 3, calculates armada Fatigue Life Scatter Factor's and safe life: assume that military service number of aircraft is n frame, tired Labor flight test vehicle is 1 frame, and logarithmic fatigue life standard deviation sigma, can by providing a large amount of fatigue data statistical results It is considered known；The random censorship data fatigue life substitution formula that step 1 is obtained:

$\underset{i=1}{\overset{r}{\mathrm{\Σ}}}\frac{(x_i-\mathrm{\μ})}{{\mathrm{\σ}}^2}+\underset{i=r+1}{\overset{n}{\mathrm{\Σ}}}\frac{{\∫}_{x_i}^{\mathrm{\∞}}\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}{e}^{-\frac{1}{2}{\left(\frac{t-\mathrm{\μ}}{\mathrm{\σ}}\right)}^2}\frac{t-\mathrm{\μ}}{{\mathrm{\σ}}^2}dt}{{\∫}_{x_i}^{\mathrm{\∞}}\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}{e}^{-\frac{1}{2}{\left(\frac{t-\mathrm{\μ}}{\mathrm{\σ}}\right)}^2}dt}=0$

Above formula is utilized to estimate to obtain the estimated value of logarithmic fatigue life mathematic expectaion μI.e. there is a group of planes for 50% reliability Aircraft structure fatigue life estimation value [N₅₀] it isσ is substituted into formula with sample size n sample range+1Calculate Group of planes Fatigue Life Scatter Factor's L_f, further according to aircaft configuration safe life computing formulaCalculate and necessarily may be used By degree and the aircaft configuration safe life N under confidence level_{P, γ}。

Further, in described step 2: the specific algorithm of the Maximum-likelihood estimation of lognormal distribution parameter is:

To μ, σ Derivation respectively:

$\frac{\∂\ln L}{\∂\mathrm{\μ}}=\underset{i=1}{\overset{r}{\mathrm{\Σ}}}\frac{(x_i-\mathrm{\μ})}{{\mathrm{\σ}}^2}+\underset{i=r+1}{\overset{n}{\mathrm{\Σ}}}\frac{{\∫}_{x_i}^{\mathrm{\∞}}\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}{e}^{-\frac{1}{2}{\left(\frac{t-\mathrm{\μ}}{\mathrm{\σ}}\right)}^2}\frac{t-\mathrm{\μ}}{{\mathrm{\σ}}^2}dt}{{\∫}_{x_i}^{\mathrm{\∞}}\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}{e}^{-\frac{1}{2}{\left(\frac{t-\mathrm{\μ}}{\mathrm{\σ}}\right)}^2}dt}$

$\frac{\∂\ln L}{\∂\mathrm{\σ}}=-\frac{n}{\mathrm{\σ}}+\underset{i=1}{\overset{r}{\mathrm{\Σ}}}\frac{{(x_i-\mathrm{\μ})}^2}{{\mathrm{\σ}}^3}+\underset{i=r+1}{\overset{n}{\mathrm{\Σ}}}\frac{{\∫}_{x_i}^{\mathrm{\∞}}{e}^{-\frac{1}{2}{\left(\frac{t-\mathrm{\μ}}{\mathrm{\σ}}\right)}^2}\frac{{(t-\mathrm{\μ})}^2}{{\mathrm{\σ}}^2}dt}{\mathrm{\σ}{\∫}_{x_i}^{\mathrm{\∞}}{e}^{-\frac{1}{2}{\left(\frac{t-\mathrm{\μ}}{\mathrm{\σ}}\right)}^2}dt}$

OrderEquation below:

$\begin{array}{c}\underset{i=1}{\overset{r}{\mathrm{\Σ}}}\frac{(x_i-\mathrm{\μ})}{{\mathrm{\σ}}^2}+\underset{i=r+1}{\overset{n}{\mathrm{\Σ}}}\frac{{\∫}_{x_i}^{\mathrm{\∞}}\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}{e}^{-\frac{1}{2}{\left(\frac{t-\mathrm{\μ}}{\mathrm{\σ}}\right)}^2}\frac{t-\mathrm{\μ}}{{\mathrm{\σ}}^2}dt}{{\∫}_{x_i}^{\mathrm{\∞}}\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}{e}^{-\frac{1}{2}{\left(\frac{t-\mathrm{\μ}}{\mathrm{\σ}}\right)}^2}dt}=0\\ -\frac{n}{\mathrm{\σ}}+\underset{i=1}{\overset{r}{\mathrm{\Σ}}}\frac{{(x_i-\mathrm{\μ})}^2}{{\mathrm{\σ}}^3}+\underset{i=r+1}{\overset{n}{\mathrm{\Σ}}}\frac{{\∫}_{x_i}^{\mathrm{\∞}}{e}^{-\frac{1}{2}{\left(\frac{t-\mathrm{\μ}}{\mathrm{\σ}}\right)}^2}\frac{{(t-\mathrm{\μ})}^2}{{\mathrm{\σ}}^2}dt}{\mathrm{\σ}{\∫}_{x_i}^{\mathrm{\∞}}{e}^{-\frac{1}{2}{\left(\frac{t-\mathrm{\μ}}{\mathrm{\σ}}\right)}^2}dt}=0.\end{array}$

Further, described aircaft configuration safe life based on test and use data fusion of being on active service determines that method is entered One step includes that homotype aircraft group of planes safe life under same test load is composed determines method, and step is:

Calculate military service CALCULATING STRUCTURAL FATIGUE DAMAGE OF AIRCRAFT value and equivalent pilot time or the number of times that rises and falls；

Obtain aircaft configuration random censorship data fatigue life；

Calculate aircraft structure fatigue life distribution function parameter；

Calculate armada Fatigue Life Scatter Factor's and safe life.

Further, described homotype aircraft group of planes safe life under same test load is composed determines method concrete steps For:

Step 1, calculates military service CALCULATING STRUCTURAL FATIGUE DAMAGE OF AIRCRAFT value and equivalent pilot time or the number of times that rises and falls: for non-linear tired Tired meter defect theory, the damage measurement formula that n cyclic loading causes is:

$D=\underset{i=1}{\overset{p}{\mathrm{\Σ}}}\frac{n_i}{N_1{\left(\frac{S_1}{S_i}\right)}^d}$

S in formula₁For load once maximum in the load series before this load cycle；N₁For corresponding to S₁Fatigue Life-span；n_iFor the cycle-index of i-stage load,D is material constant；Carten and Dolan is based on fatigue test Data are advised: for high strength steel: d=4.8；Other material: d=5.8；

For full machine fatigue test, when testpieces destroys, equivalent damage can be obtained for D₁；It is to say, D is damaged under experimental condition₁Correspond to one fatigue life N₁, then its per pilot time equivalent impairment value is:

$k_1=\frac{D_1}{N_1}$

Using identical equivalent damage measurement method calculating every frame under practical flight loading spectrum to be on active service uses flight little Time N_iEquivalent impairment value D corresponding to aircaft configuration_i, then its per pilot time equivalent impairment value is:

$k_i=\frac{D_i}{N_i}$

Then the conversion factor at equivalent pilot time is:

$k_{1,i}=\frac{k_1}{k_i}$

Utilize military service aircraft practical flight hour to be multiplied by conversion factor and just obtain this airplane working as under test load is composed Amount pilot time number；

Step 2, acquisition aircaft configuration random censorship data fatigue life: military service aircraft equivalent pilot time number and test The aircraft fatigue life-span takes the logarithm later from same distribution, it is believed that be random censorship data fatigue life；

Step 3, calculating aircraft structure fatigue life distribution function parameter: the logarithm normal distribution under random censorship situation Likelihood function and the Maximum-likelihood estimation of lognormal distribution parameter；

Step 4, calculating armada Fatigue Life Scatter Factor's and safe life:

Assuming that military service number of aircraft is n frame, fatigue test aircraft is 1 frame, and logarithmic fatigue life standard deviation sigma is by tired Labor test data statistical result is given, it is believed that be known；The random censorship data fatigue life generation that step 2 is obtained Enter formula:

$\underset{i=1}{\overset{r}{\mathrm{\Σ}}}\frac{(x_i-\mathrm{\μ})}{{\mathrm{\σ}}^2}+\underset{i=r+1}{\overset{n}{\mathrm{\Σ}}}\frac{{\∫}_{x_i}^{\mathrm{\∞}}\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}{e}^{-\frac{1}{2}{\left(\frac{t-\mathrm{\μ}}{\mathrm{\σ}}\right)}^2}\frac{t-\mathrm{\μ}}{{\mathrm{\σ}}^2}dt}{{\∫}_{x_i}^{\mathrm{\∞}}\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}{e}^{-\frac{1}{2}{\left(\frac{t-\mathrm{\μ}}{\mathrm{\σ}}\right)}^2}dt}=0$

Above formula is utilized to estimate to obtain the estimated value of logarithmic fatigue life mathematic expectaion μI.e. there is the aircraft of 50% reliability Structure fatigue life estimated value [N₅₀] it isσ is substituted into formula with sample size n sample range+1Calculate Group of planes Fatigue Life Scatter Factor's L_f, further according to aircaft configuration safe life computing formulaCalculate and necessarily may be used By degree and the aircaft configuration safe life N under confidence level_{P, γ}。

Further, in described step 3: the logarithm normal distribution likelihood function under random censorship situation calculates concrete step Suddenly it is:

If the distribution function of life-span X is F (x, θ) (θ ∈ Θ), density function be f (x, θ), Θ be the non-NULL opener in R, From distribution function be F (x, θ) overall in, randomly draw n individual, carry out life test；For each individuality, observe the life-span It is X_i(i=1 ..., n), correspondingly there is individual truncated time Y_i(i=1 ..., n), observation X that i-th individuality is obtained by we_i ∧Y_iTake minima, make t_i=X_i∧Y_i,So can be obtained by data (t_i, δ_i) (i=1 ..., n), δ_i=1 Represent t_iIt is test failure data, δ_i=0 represents t_iIt it is non-failure data；Then data (t₁, δ₁) ..., (t_n, δ_n) likelihood function For:

$L\left(\mathrm{\θ}\right)=\underset{i=1}{\overset{n}{\mathrm{\Π}}}f{(t_i,\mathrm{\θ})}^{{\mathrm{\δ}}_i}{\[1-F(t_i,\mathrm{\θ})\]}^{1-{\mathrm{\δ}}_i}$

If N fatigue life of aircraft obeys logarithm normal distribution, then can be designated as

LgN=X～N (μ, σ²)

Distribution function and density function are respectively as follows:

$F\left(x\right)={\∫}_0^x\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}{e}^{-\frac{{(t-u)}^2}{2{\mathrm{\σ}}^2}}dt$

$f\left(x\right)=\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}{e}^{-\frac{{(x-\mathrm{\μ})}^2}{2{\mathrm{\σ}}^2}}$

X_i(i=1 ..., r) it is fatigue failure life, X_i(i=r+1 ..., n) it is the tired no-failure life-span；Then likelihood function For:

$\begin{array}{c}L\left(\mathrm{\θ}\right)=\underset{i=1}{\overset{n}{\mathrm{\Π}}}f{(t_i,\mathrm{\θ})}^{{\mathrm{\δ}}_i}{\[1-F(t_i,\mathrm{\θ})\]}^{1-{\mathrm{\δ}}_i}\\ =\frac{1}{{\left(\sqrt{2\mathrm{\π}}\mathrm{\σ}\right)}^r}{e}^{-\underset{i=1}{\overset{r}{\mathrm{\Σ}}}\frac{{(x_i-\mathrm{\μ})}^2}{2{\mathrm{\σ}}^2}}\underset{i=r+1}{\overset{n}{\mathrm{\Π}}}\[{\∫}_{x_i}^{\mathrm{\∞}}\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}{e}^{-\frac{1}{2}{\left(\frac{t-\mathrm{\μ}}{\mathrm{\σ}}\right)}^2}dt\].\end{array}$

Further, in described step 3: the specific algorithm of the Maximum-likelihood estimation of lognormal distribution parameter is:

To μ, σ derivation respectively:

$\begin{array}{c}\frac{\∂\ln L}{\∂\mathrm{\μ}}=\underset{i=1}{\overset{r}{\mathrm{\Σ}}}\frac{(x_i-\mathrm{\μ})}{{\mathrm{\σ}}^2}+\underset{i=r+1}{\overset{n}{\mathrm{\Σ}}}\frac{{\∫}_{x_i}^{\mathrm{\∞}}\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}{e}^{-\frac{1}{2}{\left(\frac{t-\mathrm{\μ}}{\mathrm{\σ}}\right)}^2}\frac{t-\mathrm{\μ}}{{\mathrm{\σ}}^2}dt}{{\∫}_{x_i}^{\mathrm{\∞}}\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}{e}^{-\frac{1}{2}{\left(\frac{t-\mathrm{\μ}}{\mathrm{\σ}}\right)}^2}dt}\\ \frac{\∂\ln L}{\∂\mathrm{\σ}}=-\frac{n}{\mathrm{\σ}}+\underset{i=1}{\overset{r}{\mathrm{\Σ}}}\frac{{(x_i-\mathrm{\μ})}^2}{{\mathrm{\σ}}^3}+\underset{i=r+1}{\overset{n}{\mathrm{\Σ}}}\frac{{\∫}_{x_i}^{\mathrm{\∞}}{e}^{-\frac{1}{2}{\left(\frac{t-\mathrm{\μ}}{\mathrm{\σ}}\right)}^2}\frac{{(t-\mathrm{\μ})}^2}{{\mathrm{\σ}}^2}dt}{\mathrm{\σ}{\∫}_{x_i}^{\mathrm{\∞}}{e}^{-\frac{1}{2}{\left(\frac{t-\mathrm{\μ}}{\mathrm{\σ}}\right)}^2}dt}\end{array}$

OrderEquation below:

$\begin{array}{c}\underset{i=1}{\overset{r}{\mathrm{\Σ}}}\frac{(x_i-\mathrm{\μ})}{{\mathrm{\σ}}^2}+\underset{i=r+1}{\overset{n}{\mathrm{\Σ}}}\frac{{\∫}_{x_i}^{\mathrm{\∞}}\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}{e}^{-\frac{1}{2}{\left(\frac{t-\mathrm{\μ}}{\mathrm{\σ}}\right)}^2}\frac{t-\mathrm{\μ}}{{\mathrm{\σ}}^2}dt}{{\∫}_{x_i}^{\mathrm{\∞}}\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}{e}^{-\frac{1}{2}{\left(\frac{t-\mathrm{\μ}}{\mathrm{\σ}}\right)}^2}dt}=0\\ -\frac{n}{\mathrm{\σ}}+\underset{i=1}{\overset{r}{\mathrm{\Σ}}}\frac{{(x_i-\mathrm{\μ})}^2}{{\mathrm{\σ}}^3}+\underset{i=r+1}{\overset{n}{\mathrm{\Σ}}}\frac{{\∫}_{x_i}^{\mathrm{\∞}}{e}^{-\frac{1}{2}{\left(\frac{t-\mathrm{\μ}}{\mathrm{\σ}}\right)}^2}\frac{{(t-\mathrm{\μ})}^2}{{\mathrm{\σ}}^2}dt}{\mathrm{\σ}{\∫}_{x_i}^{\mathrm{\∞}}{e}^{-\frac{1}{2}{\left(\frac{t-\mathrm{\μ}}{\mathrm{\σ}}\right)}^2}dt}=0.\end{array}$

A kind of based on test and use data fusion of being on active service the aircaft configuration safe life of the present invention determines method, including When homotype aircraft different loads spectrum lower test data fatigue life and use data fatigue life of being on active service obey logarithm normal distribution Group of planes safe life determines that method and the homotype aircraft group of planes safe life under same test load is composed determines method.Homotype flies Group of planes peace when machine different loads spectrum lower test data fatigue life and use data fatigue life of being on active service obey logarithm normal distribution Life-cycle determines that method comprises the following steps: obtain aircaft configuration random censorship data fatigue life；Calculating aircaft configuration is tired Labor life distribution function parameter；Calculate armada Fatigue Life Scatter Factor's and safe life.Homotype aircraft is in same test Group of planes safe life under loading spectrum determines that method comprises the following steps: calculate military service CALCULATING STRUCTURAL FATIGUE DAMAGE OF AIRCRAFT value and equivalent flies Row hour or the number of times that rises and falls；Obtain aircaft configuration random censorship data fatigue life；Calculate the distribution of aircraft structure fatigue life-span Function parameter；Calculate the armada fatigue coefficient of dispersion and safe life.The present invention is directed to homotype aircaft configuration due to group of planes clothes When using as a servant the difference of maneuvering load and cause the aircraft structure fatigue life-span to obey logarithm normal distribution, the random censorship of military service aircraft Lifetime data can with flight test vehicle test life data directly merge for carry out Reliability Analysis of Aircraft Structure with Calculate；The aircraft structure fatigue life-span is caused to be disobeyed for homotype aircaft configuration due to the difference of group of planes military service maneuvering load right During number normal distribution, the method using EQUIVALENT DAMAGE CONVERSION, the real load environment of military service aircraft is equivalent to flight test vehicle and carries Lotus environmental treatment, is converted into same parent statistical problem becoming parent statistical problem；Owing to the data of military service aircraft are brought into During aircaft configuration safe life is analyzed, sample size increases, and improves the accuracy of Reliability Analysis of Aircraft Structure；Use random Likelihood function estimation sample life-span average [N under right Random Truncation₅₀], and then calculate certain reliability and flying under confidence level Machine structural safety life-span N_{P, γ}, calculate for group of planes safe life and provide a kind of reference method；The aircraft knot calculated according to the present invention Structure safe life may be used in group of planes life-span management and unit life-span management.

Additionally, be the accuracy improving further Reliability Analysis of Aircraft Structure, under arms aircraft can randomly draw 1 frame Or several planes proceeds full machine fatigue test under test load is composed.Extract the military service aircraft flight of full machine fatigue test Hourage equivalent pilot time number under equivalent conversion to test load is composed, then total fatigue test life-span is that equivalent flight is little Time number and full machine fatigue test life-span sum.The full machine fatigue test results of multi-aircraft is on active service with military service aircraft again and uses number Reliability Analysis of Aircraft Structure is carried out according to fusion.Now, the increasing number of full machine fatigue test aircraft, aircraft structural reliability divides The accuracy of analysis will further improve.A kind of basic skills that the inventive method can be determined as military service aircaft configuration, lengthen the life.

Accompanying drawing explanation

Fig. 1 is that under the homotype aircraft different loads spectrum that the embodiment of the present invention provides, test data fatigue life and military service use When fatigue life, data obeyed logarithm normal distribution, group of planes safe life determines the flow chart of method；

Fig. 2 is that the homotype aircraft equivalent of embodiment of the present invention offer group of planes safe life under same test load is composed is true Determine the flow chart of method.

Detailed description of the invention

In order to make the purpose of the present invention, technical scheme and advantage clearer, below in conjunction with embodiment, to the present invention It is further elaborated.Should be appreciated that specific embodiment described herein, only in order to explain the present invention, is not used to Limit the present invention.

Fig. 1 shows that under the homotype aircraft different loads spectrum that the present invention provides, test data fatigue life and use of being on active service are tired When labor lifetime data obeys logarithm normal distribution, group of planes safe life determines the flow process of method.For convenience of description, only illustrate Part related to the present invention.

Homotype aircraft different loads spectrum lower test data fatigue life and military service that embodiments of the invention provide use tired When labor lifetime data obeys logarithm normal distribution, group of planes safe life determines that method, the method comprise the following steps:

Obtain aircaft configuration random censorship data fatigue life；

Calculate aircraft structure fatigue life distribution function parameter；

Calculate armada Fatigue Life Scatter Factor's and safe life.

As a prioritization scheme of the embodiment of the present invention, lower test data fatigue life of homotype aircraft different loads spectrum and clothes Use and determine that method concretely comprises the following steps with group of planes safe life when fatigue life, data obeyed logarithm normal distribution:

Step 1, obtains aircaft configuration random censorship data fatigue life: test fatigue under homotype aircraft different loads spectrum When lifetime data and use data fatigue life of being on active service obey logarithm normal distribution, it is believed that consider structure and loading spectrum dispersion Property and aircraft structure fatigue life-span of causing also describes by logarithm normal distribution, so tired with the lower flight test vehicle of different loads spectrum Lifetime data uses aircraft fatigue lifetime data to directly obtain aircaft configuration random censorship fatigue life after taking the logarithm with being on active service Data；

Step 2, calculating aircraft structure fatigue life distribution function parameter: the logarithm normal distribution under random censorship situation Likelihood function and the Maximum-likelihood estimation of lognormal distribution parameter；

Step 3, calculates armada Fatigue Life Scatter Factor's and safe life: assume that military service number of aircraft is n frame, entirely Machine fatigue test aircraft is 1 frame, and logarithmic fatigue life standard deviation sigma is by providing a large amount of fatigue data statistical results , it is believed that it is known.The random censorship lifetime data substitution formula that step 1 is obtained:

$\underset{i=1}{\overset{r}{\mathrm{\Σ}}}\frac{(x_i-\mathrm{\μ})}{{\mathrm{\σ}}^2}+\underset{i=r+1}{\overset{n}{\mathrm{\Σ}}}\frac{{\∫}_{x_i}^{\mathrm{\∞}}\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}{e}^{-\frac{1}{2}{\left(\frac{t-\mathrm{\μ}}{\mathrm{\σ}}\right)}^2}\frac{t-\mathrm{\μ}}{{\mathrm{\σ}}^2}dt}{{\∫}_{x_i}^{\mathrm{\∞}}\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}{e}^{-\frac{1}{2}{\left(\frac{t-\mathrm{\μ}}{\mathrm{\σ}}\right)}^2}dt}=0$

Above formula is utilized to estimate to obtain the estimated value of logarithmic fatigue life mathematic expectaion μI.e. there is a group of planes for 50% reliability Aircraft structure fatigue life estimation value [N₅₀] it isσ is substituted into formula with sample size n sample range+1Calculate Group of planes Fatigue Life Scatter Factor's L_f, further according to aircaft configuration safe life computing formulaCalculate certain Reliability and the aircaft configuration safe life N under confidence level_{P, γ}。

As a prioritization scheme of the embodiment of the present invention, in step 2: the logarithm normal distribution under random censorship situation Likelihood function calculates and concretely comprises the following steps:

If the distribution function of life-span X is F (x, θ) (θ ∈ Θ), density function be f (x, θ), Θ be the non-NULL opener in R, From distribution function be F (x, θ) overall in, randomly draw n individual, carry out life test.For each individuality, observe the life-span It is X_i(i=1 ..., n), correspondingly there is individual truncated time Y_i(i=1 ..., n), observation X that i-th individuality is obtained by we_i ∧Y_iTake minima, make t_i=X_i∧Y_i,So can be obtained by data (t_i, δ_i) (i=1 ..., n), δ_i=1 Represent t_iIt is test failure data, δ_i=0 represents t_iIt it is non-failure data.Then data (t₁, δ₁) ..., (t_n, δ_n) likelihood function For:

$L\left(\mathrm{\θ}\right)=\underset{i=1}{\overset{n}{\mathrm{\Π}}}f{(t_i,\mathrm{\θ})}^{{\mathrm{\δ}}_i}{\[1-F(t_i,\mathrm{\θ})\]}^{1-{\mathrm{\δ}}_i}$

If N fatigue life of aircraft obeys logarithm normal distribution, then can be designated as

LgN=X～N (μ, σ²)

Distribution function and density function are respectively as follows:

$F\left(x\right)={\∫}_0^x\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}{e}^{-\frac{{(t-u)}^2}{2{\mathrm{\σ}}^2}}dt$

$f\left(x\right)=\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}{e}^{-\frac{{(x-\mathrm{\μ})}^2}{2{\mathrm{\σ}}^2}}$

X_i(i=1 ..., r) it is fatigue failure life, X_i(i=r+1 ..., n) it is the tired no-failure life-span.Then likelihood function For:

$\begin{array}{c}L\left(\mathrm{\θ}\right)=\underset{i=1}{\overset{n}{\mathrm{\Π}}}f{(t_i,\mathrm{\θ})}^{{\mathrm{\δ}}_i}{\[1-F(t_i,\mathrm{\θ})\]}^{1-{\mathrm{\δ}}_i}\\ =\frac{1}{{\left(\sqrt{2\mathrm{\π}}\mathrm{\σ}\right)}^r}{e}^{-\underset{i=1}{\overset{r}{\mathrm{\Σ}}}\frac{{(x_i-\mathrm{\μ})}^2}{2{\mathrm{\σ}}^2}}\underset{i=r+1}{\overset{n}{\mathrm{\Π}}}\[{\∫}_{x_i}^{\mathrm{\∞}}\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}{e}^{-\frac{1}{2}{\left(\frac{t-\mathrm{\μ}}{\mathrm{\σ}}\right)}^2}dt\].\end{array}$

As a prioritization scheme of the embodiment of the present invention, in step 2: the Maximum-likelihood estimation of lognormal distribution parameter Specific algorithm be:

$\ln L=-\frac{r}{2}\ln 2\mathrm{\π}-r\ln \mathrm{\σ}-\underset{i=1}{\overset{r}{\mathrm{\Σ}}}\frac{{(x_i-\mathrm{\μ})}^2}{2{\mathrm{\σ}}^2}+\underset{i=r+1}{\overset{n}{\mathrm{\Σ}}}\ln \[{\∫}_{x_i}^{\mathrm{\∞}}\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}{e}^{-\frac{1}{2}{\left(\frac{t-\mathrm{\μ}}{\mathrm{\σ}}\right)}^2}dt\]$

To μ, σ derivation respectively:

$\begin{array}{c}\frac{\∂\ln L}{\∂\mathrm{\μ}}=\underset{i=1}{\overset{r}{\mathrm{\Σ}}}\frac{(x_i-\mathrm{\μ})}{{\mathrm{\σ}}^2}+\underset{i=r+1}{\overset{n}{\mathrm{\Σ}}}\frac{{\∫}_{x_i}^{\mathrm{\∞}}\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}{e}^{-\frac{1}{2}{\left(\frac{t-\mathrm{\μ}}{\mathrm{\σ}}\right)}^2}\frac{t-\mathrm{\μ}}{{\mathrm{\σ}}^2}dt}{{\∫}_{x_i}^{\mathrm{\∞}}\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}{e}^{-\frac{1}{2}{\left(\frac{t-\mathrm{\μ}}{\mathrm{\σ}}\right)}^2}dt}\\ \frac{\∂\ln L}{\∂\mathrm{\σ}}=-\frac{n}{\mathrm{\σ}}+\underset{i=1}{\overset{r}{\mathrm{\Σ}}}\frac{{(x_i-\mathrm{\μ})}^2}{{\mathrm{\σ}}^3}+\underset{i=r+1}{\overset{n}{\mathrm{\Σ}}}\frac{{\∫}_{x_i}^{\mathrm{\∞}}{e}^{-\frac{1}{2}{\left(\frac{t-\mathrm{\μ}}{\mathrm{\σ}}\right)}^2}\frac{{(t-\mathrm{\μ})}^2}{{\mathrm{\σ}}^2}dt}{\mathrm{\σ}{\∫}_{x_i}^{\mathrm{\∞}}{e}^{-\frac{1}{2}{\left(\frac{t-\mathrm{\μ}}{\mathrm{\σ}}\right)}^2}dt}\end{array}$

OrderEquation below:

$\begin{array}{c}\underset{i=1}{\overset{r}{\mathrm{\Σ}}}\frac{(x_i-\mathrm{\μ})}{{\mathrm{\σ}}^2}+\underset{i=r+1}{\overset{n}{\mathrm{\Σ}}}\frac{{\∫}_{x_i}^{\mathrm{\∞}}\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}{e}^{-\frac{1}{2}{\left(\frac{t-\mathrm{\μ}}{\mathrm{\σ}}\right)}^2}\frac{t-\mathrm{\μ}}{{\mathrm{\σ}}^2}dt}{{\∫}_{x_i}^{\mathrm{\∞}}\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}{e}^{-\frac{1}{2}{\left(\frac{t-\mathrm{\μ}}{\mathrm{\σ}}\right)}^2}dt}=0\\ -\frac{n}{\mathrm{\σ}}+\underset{i=1}{\overset{r}{\mathrm{\Σ}}}\frac{{(x_i-\mathrm{\μ})}^2}{{\mathrm{\σ}}^3}+\underset{i=r+1}{\overset{n}{\mathrm{\Σ}}}\frac{{\∫}_{x_i}^{\mathrm{\∞}}{e}^{-\frac{1}{2}{\left(\frac{t-\mathrm{\μ}}{\mathrm{\σ}}\right)}^2}\frac{{(t-\mathrm{\μ})}^2}{{\mathrm{\σ}}^2}dt}{\mathrm{\σ}{\∫}_{x_i}^{\mathrm{\∞}}{e}^{-\frac{1}{2}{\left(\frac{t-\mathrm{\μ}}{\mathrm{\σ}}\right)}^2}dt}=0\end{array}$

Below in conjunction with the accompanying drawings and the application principle of the present invention is further described by specific embodiment.

As it is shown in figure 1, lower test data fatigue life of the homotype aircraft different loads spectrum of the embodiment of the present invention and military service make Determine that method comprises the following steps with group of planes safe life when fatigue life, data obeyed logarithm normal distribution:

S101: obtain aircaft configuration random censorship data fatigue life；

S102: calculate aircraft structure fatigue life distribution function parameter；

S103: calculate armada Fatigue Life Scatter Factor's and safe life.

Homotype aircraft different loads spectrum lower test data fatigue life of the present invention and use data fatigue life clothes of being on active service When logarithm normal distribution, group of planes safe life determines concretely comprising the following steps of method:

Step 1, acquisition aircaft configuration random censorship data fatigue life:

Homotype aircraft different loads spectrum lower test data fatigue life and use data fatigue life of being on active service just are obeying logarithm During state distribution, it is believed that consider structure and loading spectrum dispersibility and aircraft structure fatigue life-span of causing also divides by lognormal Cloth describes, so using aircraft fatigue lifetime data to take the logarithm by lower flight test vehicle data fatigue life of different loads spectrum with being on active service After directly obtain aircaft configuration random censorship data fatigue life；

Step 2, calculating aircraft structure fatigue life distribution function parameter:

Step (a): the logarithm normal distribution likelihood function under random censorship situation:

If the distribution function of life-span X is F (x, θ) (θ ∈ Θ), density function be f (x, θ), Θ be the non-NULL opener in R, From distribution function be F (x, θ) overall in, randomly draw n individual, carry out life test.For each individual observation life-span It is X_i(i=1 ..., n), correspondingly there is individual truncated time Y_i(i=1 ..., n), observation X that i-th individuality is obtained by we_i ∧Y_i(taking minima), makes t_i=X_i∧Y_i,So can be obtained by data (t_i, δ_i) (i=1 ..., n), δ_i =1 represents t_iIt is test failure data, δ_i=0 represents t_iIt it is non-failure data.Then data (t₁, δ₁) ..., (t_n, δ_n) likelihood Function is:

$L\left(\mathrm{\θ}\right)=\underset{i=1}{\overset{n}{\mathrm{\Π}}}f{(t_i,\mathrm{\θ})}^{{\mathrm{\δ}}_i}{\[1-F(t_i,\mathrm{\θ})\]}^{1-{\mathrm{\δ}}_i}$

If N fatigue life of aircraft obeys logarithm normal distribution, then can be designated as

LgN=X～N (μ, σ²)

Distribution function and density function are respectively as follows:

$F\left(x\right)={\∫}_0^x\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}{e}^{-\frac{{(t-u)}^2}{2{\mathrm{\σ}}^2}}dt$

$f\left(x\right)=\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}{e}^{-\frac{{(x-\mathrm{\μ})}^2}{2{\mathrm{\σ}}^2}}$

X_i(i=1 ..., r) it is fatigue failure life, X_i(i=r+1 ..., n) it is the tired no-failure life-span.Then likelihood function For:

$\begin{array}{c}L\left(\mathrm{\θ}\right)=\underset{i=1}{\overset{n}{\mathrm{\Π}}}f{(t_i,\mathrm{\θ})}^{{\mathrm{\δ}}_i}{\[1-F(t_i,\mathrm{\θ})\]}^{1-{\mathrm{\δ}}_i}\\ =\frac{1}{{\left(\sqrt{2\mathrm{\π}}\mathrm{\σ}\right)}^r}{e}^{-\underset{i=1}{\overset{r}{\mathrm{\Σ}}}\frac{{(x_i-\mathrm{\μ})}^2}{2{\mathrm{\σ}}^2}}\underset{i=r+1}{\overset{n}{\mathrm{\Π}}}\[{\∫}_{x_i}^{\mathrm{\∞}}\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}{e}^{-\frac{1}{2}{\left(\frac{t-\mathrm{\μ}}{\mathrm{\σ}}\right)}^2}dt\]\end{array}$

Step (b): the Maximum-likelihood estimation of lognormal distribution parameter:

$\ln L=-\frac{r}{2}\ln 2\mathrm{\π}-r\ln \mathrm{\σ}-\underset{i=1}{\overset{r}{\mathrm{\Σ}}}\frac{{(x_i-\mathrm{\μ})}^2}{2{\mathrm{\σ}}^2}+\underset{i=r+1}{\overset{n}{\mathrm{\Σ}}}\ln \[{\∫}_{x_i}^{\mathrm{\∞}}\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}{e}^{-\frac{1}{2}{\left(\frac{t-\mathrm{\μ}}{\mathrm{\σ}}\right)}^2}dt\]$

To μ, σ derivation respectively:

$\frac{\∂\ln L}{\∂\mathrm{\μ}}=\underset{i=1}{\overset{r}{\mathrm{\Σ}}}\frac{(x_i-\mathrm{\μ})}{{\mathrm{\σ}}^2}+\underset{i=r+1}{\overset{n}{\mathrm{\Σ}}}\frac{{\∫}_{x_i}^{\mathrm{\∞}}\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}{e}^{-\frac{1}{2}{\left(\frac{t-\mathrm{\μ}}{\mathrm{\σ}}\right)}^2}\frac{t-\mathrm{\μ}}{{\mathrm{\σ}}^2}dt}{{\∫}_{x_i}^{\mathrm{\∞}}\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}{e}^{-\frac{1}{2}{\left(\frac{t-\mathrm{\μ}}{\mathrm{\σ}}\right)}^2}dt}$

$\frac{\∂\ln L}{\∂\mathrm{\σ}}=-\frac{n}{\mathrm{\σ}}+\underset{i=1}{\overset{r}{\mathrm{\Σ}}}\frac{{(x_i-\mathrm{\μ})}^2}{{\mathrm{\σ}}^3}+\underset{i=r+1}{\overset{n}{\mathrm{\Σ}}}\frac{{\∫}_{x_i}^{\mathrm{\∞}}{e}^{-\frac{1}{2}{\left(\frac{t-\mathrm{\μ}}{\mathrm{\σ}}\right)}^2}\frac{{(t-\mathrm{\μ})}^2}{{\mathrm{\σ}}^2}dt}{\mathrm{\σ}{\∫}_{x_i}^{\mathrm{\∞}}{e}^{-\frac{1}{2}{\left(\frac{t-\mathrm{\μ}}{\mathrm{\σ}}\right)}^2}dt}$

OrderEquation below:

$\begin{array}{c}\underset{i=1}{\overset{r}{\mathrm{\Σ}}}\frac{(x_i-\mathrm{\μ})}{{\mathrm{\σ}}^2}+\underset{i=r+1}{\overset{n}{\mathrm{\Σ}}}\frac{{\∫}_{x_i}^{\mathrm{\∞}}\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}{e}^{-\frac{1}{2}{\left(\frac{t-\mathrm{\μ}}{\mathrm{\σ}}\right)}^2}\frac{t-\mathrm{\μ}}{{\mathrm{\σ}}^2}dt}{{\∫}_{x_i}^{\mathrm{\∞}}\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}{e}^{-\frac{1}{2}{\left(\frac{t-\mathrm{\μ}}{\mathrm{\σ}}\right)}^2}dt}=0\\ -\frac{n}{\mathrm{\σ}}+\underset{i=1}{\overset{r}{\mathrm{\Σ}}}\frac{{(x_i-\mathrm{\μ})}^2}{{\mathrm{\σ}}^3}+\underset{i=r+1}{\overset{n}{\mathrm{\Σ}}}\frac{{\∫}_{x_i}^{\mathrm{\∞}}{e}^{-\frac{1}{2}{\left(\frac{t-\mathrm{\μ}}{\mathrm{\σ}}\right)}^2}\frac{{(t-\mathrm{\μ})}^2}{{\mathrm{\σ}}^2}dt}{\mathrm{\σ}{\∫}_{x_i}^{\mathrm{\∞}}{e}^{-\frac{1}{2}{\left(\frac{t-\mathrm{\μ}}{\mathrm{\σ}}\right)}^2}dt}=0\end{array}$

Step 3, calculating armada Fatigue Life Scatter Factor's and safe life:

Assuming that military service number of aircraft is n frame, full machine fatigue test aircraft is 1 frame, and logarithmic fatigue life standard deviation sigma is to pass through A large amount of fatigue data statistical results are given, it is believed that be known.The random censorship life-span number that step 1 is obtained According to substituting into formula:

$\underset{i=1}{\overset{r}{\mathrm{\Σ}}}\frac{(x_i-\mathrm{\μ})}{{\mathrm{\σ}}^2}+\underset{i=r+1}{\overset{n}{\mathrm{\Σ}}}\frac{{\∫}_{x_i}^{\mathrm{\∞}}\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}{e}^{-\frac{1}{2}{\left(\frac{t-\mathrm{\μ}}{\mathrm{\σ}}\right)}^2}\frac{t-\mathrm{\μ}}{{\mathrm{\σ}}^2}dt}{{\∫}_{x_i}^{\mathrm{\∞}}\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}{e}^{-\frac{1}{2}{\left(\frac{t-\mathrm{\μ}}{\mathrm{\σ}}\right)}^2}dt}=0$

Above formula is utilized to estimate to obtain the estimated value of logarithmic fatigue life mathematic expectaion μI.e. there is a group of planes for 50% reliability Aircraft structure fatigue life estimation value [N₅₀] it isσ is substituted into formula with sample size n sample range+1Meter Calculate group of planes Fatigue Life Scatter Factor's L_f, further according to aircaft configuration safe life computing formulaCalculate certain Reliability and the aircaft configuration safe life N under confidence level_{P, γ}。

As in figure 2 it is shown, the group of planes safe life that the homotype aircraft of the embodiment of the present invention is under same test load is composed determines Method comprises the following steps:

S201: calculate military service CALCULATING STRUCTURAL FATIGUE DAMAGE OF AIRCRAFT value and equivalent pilot time or the number of times that rises and falls；

S202: obtain aircaft configuration random censorship data fatigue life；

S203: calculate aircraft structure fatigue life distribution function parameter；

S204: calculate armada Fatigue Life Scatter Factor's and safe life.

The homotype aircraft of embodiment of the present invention group of planes safe life under same test load is composed determines that method specifically walks Suddenly it is:

Step 1, calculates military service CALCULATING STRUCTURAL FATIGUE DAMAGE OF AIRCRAFT value and equivalent pilot time or the number of times that rises and falls: for non-linear tired Tired meter defect theory, the damage measurement formula that n cyclic loading causes is:

$D=\underset{i=1}{\overset{p}{\mathrm{\Σ}}}\frac{n_i}{N_1{\left(\frac{S_1}{S_i}\right)}^d}$

S in formula₁For load once maximum in the load series before this load cycle；N₁For corresponding to S₁Fatigue Life-span；n_iFor the cycle-index of i-stage load,D is material constant.Carten and Dolan is based on fatigue test Data are advised: for high strength steel: d=4.8；Other material: d=5.8.

For full machine fatigue test, when testpieces destroys, equivalent damage can be obtained for D₁.It is to say, D is damaged under experimental condition₁Correspond to one fatigue life N₁, then its per pilot time equivalent impairment value is:

$k_1=\frac{D_1}{N_1}$

Using identical equivalent damage measurement method calculating every frame under practical flight loading spectrum to be on active service uses flight little Time N_iEquivalent impairment value D corresponding to aircaft configuration_i, then its per pilot time equivalent impairment value is:

$k_i=\frac{D_i}{N_i}$

Then the conversion factor at equivalent pilot time is:

$k_{1,i}=\frac{k_1}{k_i}$

Utilize military service aircraft practical flight hour to be multiplied by conversion factor and just obtain this airplane working as under test load is composed Amount pilot time number.

Step 2, acquisition aircaft configuration random censorship data fatigue life: military service aircraft equivalent pilot time number and test The aircraft fatigue life-span takes the logarithm later from same distribution, it is believed that be random censorship data fatigue life；

Step 3, calculating aircraft structure fatigue life distribution function parameter:

Logarithm is obeyed with homotype aircraft different loads spectrum lower test data fatigue life and use data fatigue life of being on active service During normal distribution, group of planes safe life determines that the method for method step 2 is identical；

Step 4, calculating armada Fatigue Life Scatter Factor's and safe life:

Assuming that military service number of aircraft is n frame, full machine fatigue test aircraft is 1 frame, and logarithmic fatigue life standard deviation sigma is to pass through Fatigue data statistical result is given, it is believed that be known.The random censorship lifetime data generation that step 2 is obtained Enter formula:

$\underset{i=1}{\overset{r}{\mathrm{\Σ}}}\frac{(x_i-\mathrm{\μ})}{{\mathrm{\σ}}^2}+\underset{i=r+1}{\overset{n}{\mathrm{\Σ}}}\frac{{\∫}_{x_i}^{\mathrm{\∞}}\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}{e}^{-\frac{1}{2}{\left(\frac{t-\mathrm{\μ}}{\mathrm{\σ}}\right)}^2}\frac{t-\mathrm{\μ}}{{\mathrm{\σ}}^2}dt}{{\∫}_{x_i}^{\mathrm{\∞}}\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}{e}^{-\frac{1}{2}{\left(\frac{t-\mathrm{\μ}}{\mathrm{\σ}}\right)}^2}dt}=0$

Above formula is utilized to estimate to obtain the estimated value of logarithmic fatigue life mathematic expectaion μI.e. there is the aircraft of 50% reliability Structure fatigue life estimated value [N₅₀] it isσ is substituted into formula with sample size n sample range+1Computer cluster Fatigue Life Scatter Factor's L_f, further according to aircaft configuration safe life computing formulaCalculate certain reliability With the aircaft configuration safe life N under confidence level_{P, γ}。

The specific embodiment of the embodiment of the present invention:

In conjunction with embodiment, the invention will be further described:

Assuming that the aircraft structure fatigue life-span obeys logarithm normal distribution, military service number of aircraft is 9 framves, and the flight time is all 1000h, fatigue test aircraft is 1 frame, and the fatigue test life-span is 12000h.Logarithmic fatigue life standard deviation sigma is usually according to long-term Practical experience obtains, and takes the logarithmic fatigue life standard deviation sigma considering structure disperses and load scatter here₀For 0.18, take the logarithmic fatigue life standard deviation sigma only considering structure disperses_sIt is 0.12.

1, homotype aircraft different loads spectrum lower test data fatigue life and use data fatigue life of being on active service obey logarithm Group of planes safe life during normal distribution

Step 1 obtains aircaft configuration random censorship data fatigue life:

Lower flight test vehicle data fatigue life of different loads spectrum and use aircraft fatigue lifetime data of being on active service can after taking the logarithm It is considered random censorship lifetime data (include 1 test die of old age data and 9 right censored datas of no-failure), as shown in table 1.

Table 1 random censorship data fatigue life

Test/the pilot time (h)	12000 (test values)	1000	1000	1000	1000
						Random censoring data	4.0792	3	3	3	3
Test/the pilot time (h)	1000	1000	1000	1000	1000
						Random censoring data	3	3	3	3	3

Step 2 calculates aircraft structure fatigue life distribution function parameter:

Random censorship data fatigue life are utilized to carry out dividing fatigue life by the likelihood function under random censorship situation Cloth parameter estimation.

Step (a): the likelihood function of logarithm normal distribution under random censorship situation

Distribution function and density function are respectively as follows:

$F\left(x\right)={\∫}_0^x\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}{e}^{-\frac{{(t-u)}^2}{2{\mathrm{\σ}}^2}}dt$

$f\left(x\right)=\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}{e}^{-\frac{{(x-\mathrm{\μ})}^2}{2{\mathrm{\σ}}^2}}$

Then likelihood function is:

$\begin{array}{c}L\left(\mathrm{\θ}\right)=\underset{i=0}{\overset{9}{\mathrm{\Π}}}f{(t_i,\mathrm{\θ})}^{{\mathrm{\δ}}_i}{\[1-F(t_i,\mathrm{\θ})\]}^{1-{\mathrm{\δ}}_i}\\ =\frac{1}{\sqrt{2\mathrm{\π}}{\mathrm{\σ}}_0}{e}^{-\frac{{(x_0-\mathrm{\μ})}^2}{2{{\mathrm{\σ}}_0}^2}}\underset{i=1}{\overset{9}{\mathrm{\Π}}}\[{\∫}_{x_i}^{\mathrm{\∞}}\frac{1}{\sqrt{2\mathrm{\π}}{\mathrm{\σ}}_0}{e}^{-\frac{1}{2}{\left(\frac{t-\mathrm{\μ}}{{\mathrm{\σ}}_0}\right)}^2}dt\]\\ =\frac{1}{\sqrt{2\mathrm{\π}}{\mathrm{\σ}}_0}{e}^{-\frac{{(4.0792-\mathrm{\μ})}^2}{2{{\mathrm{\σ}}_0}^2}}{\left({\∫}_3^{\mathrm{\∞}}\frac{1}{\sqrt{2\mathrm{\π}}{\mathrm{\σ}}_0}{e}^{-\frac{1}{2}{\left(\frac{t-\mathrm{\μ}}{{\mathrm{\σ}}_0}\right)}^2}dt\right)}^9\end{array}$

Step (b): the Maximum-likelihood estimation of lognormal distribution parameter

Due to parent standard deviation sigma it is known that so only parameter μ is carried out maximal possibility estimation.

OrderEquation below:

$\frac{(4.0792-\mathrm{\μ})}{{{\mathrm{\σ}}_0}^2}+9\frac{{\∫}_{3.4771}^{\mathrm{\∞}}\frac{1}{\sqrt{2\mathrm{\π}}{\mathrm{\σ}}_0}{e}^{-\frac{1}{2}{\left(\frac{t-\mathrm{\μ}}{\mathrm{\σ}}\right)}^2}\frac{t-\mathrm{\μ}}{{{\mathrm{\σ}}_0}^2}dt}{{\∫}_{3.4771}^{\mathrm{\∞}}\frac{1}{\sqrt{2\mathrm{\π}}{\mathrm{\σ}}_0}{e}^{-\frac{1}{2}{\left(\frac{t-\mathrm{\μ}}{{\mathrm{\σ}}_0}\right)}^2}dt}=0$

Calculate the maximum likelihood estimation of parameter μIt is 4.0792.

Step 3 calculates armada Fatigue Life Scatter Factor's and safe life:

By σ₀=0.18 and test specimen number n=10 substitution formula calculating reliability is 99.87% and confidence level is 90% Group of planes fatigue coefficient of dispersion L_f:

$L_f={10}^{{\mathrm{\σ}}_0(u_p+\frac{u_{\mathrm{\γ}}}{\sqrt{n}})}={10}^{0.18(3+\frac{1.282}{\sqrt{10}})}=4.1$

There is the median fatigue life estimated value [N of 50% reliability₅₀]:

$\[N_{50}\]={10}^{\widehat{\mathrm{\μ}}}={10}^{4.0792}=12000.5h$

In 99.87% reliability with the aircaft configuration safe life under 90% confidence level it is:

$N_{p,\mathrm{\γ}}=\frac{\[N_{50}\]}{L_f}=\frac{12000.5}{4.1}=2926h$

2, homotype aircraft group of planes safe life under same test load is composed

Step 1 calculates military service CALCULATING STRUCTURAL FATIGUE DAMAGE OF AIRCRAFT value and equivalent pilot time:

Here we assume that the calculated every frame military service aircraft impairment value when 1000h, fatigue test aircraft exist Impairment value during 12000h and the equivalent pilot time under same test load is composed are as shown in table 2.

Table 2 fatigue damage value and equivalent pilot time

Step 2 obtains aircaft configuration random censorship data fatigue life:

The equivalent pilot time in table 2 is taken the logarithm and just obtains random censorship lifetime data (table 3):

Table 3 random censorship lifetime data

X1	X2	X3	X4	X5	X6	X7	X8	X9	X10
										4.079	2.929	2.954	2.978	3	3.021	3.041	3.061	3.079	3.097

Step 3 calculates aircraft structure fatigue life distribution function parameter:

Random censorship data fatigue life are utilized to carry out dividing fatigue life by the likelihood function under random censorship situation Cloth parameter estimation.

Step (a): the likelihood function of logarithm normal distribution under random censorship situation

Likelihood function is:

$\begin{array}{c}L\left(\mathrm{\θ}\right)=\underset{i=0}{\overset{10}{\mathrm{\Π}}}f{(t_i,\mathrm{\θ})}^{{\mathrm{\δ}}_i}{\[1-F(t_i,\mathrm{\θ})\]}^{1-{\mathrm{\δ}}_i}\\ =\frac{1}{\sqrt{2\mathrm{\π}}{\mathrm{\σ}}_s}{e}^{-\frac{{(4.0792-\mathrm{\μ})}^2}{2{{\mathrm{\σ}}_s}^2}}\underset{i=2}{\overset{10}{\mathrm{\Π}}}\[{\∫}_{x_i}^{\mathrm{\∞}}\frac{1}{\sqrt{2\mathrm{\π}}{\mathrm{\σ}}_s}{e}^{-\frac{1}{2}{\left(\frac{t-\mathrm{\μ}}{{\mathrm{\σ}}_s}\right)}^2}dt\]\end{array}$

Wherein X_i=N_i(i=2 ..., 10).

Step (b): the Maximum-likelihood estimation of lognormal distribution parameter

Due to parent standard deviation sigma it is known that so only parameter μ is carried out maximal possibility estimation.

OrderEquation below:

$\frac{(4.079-\mathrm{\μ})}{{{\mathrm{\σ}}_s}^2}+\underset{i=1}{\overset{9}{\mathrm{\Σ}}}\frac{{\∫}_{x_i}^{\mathrm{\∞}}\frac{1}{\sqrt{2\mathrm{\π}}{\mathrm{\σ}}_s}{e}^{-\frac{1}{2}{\left(\frac{t-\mathrm{\μ}}{{\mathrm{\σ}}_s}\right)}^2}\frac{t-\mathrm{\μ}}{{{\mathrm{\σ}}_s}^2}dt}{{\∫}_{x_i}^{\mathrm{\∞}}\frac{1}{\sqrt{2\mathrm{\π}}{\mathrm{\σ}}_s}{e}^{-\frac{1}{2}{\left(\frac{t-\mathrm{\μ}}{{\mathrm{\σ}}_s}\right)}^2}dt}=0$

Calculate the maximum likelihood estimation of parameter μ

Step 4 calculates armada Fatigue Life Scatter Factor's and safe life:

By σ_s=0.12 and test specimen number n=10 substitution formula calculating reliability is 99.87% and confidence level is 90% Tired coefficient of dispersion L_f:

$L_f={10}^{{\mathrm{\σ}}_s(u_p+\frac{u_{\mathrm{\γ}}}{\sqrt{n}})}={10}^{0.12(3+\frac{1.282}{\sqrt{10}})}=2.56$

There is the median fatigue life estimated value [N of 50% reliability₅₀]:

$\[N_{50}\]={10}^{\widehat{\mathrm{\μ}}}={10}^{4.0792}=12000.5h$

In 99.87% reliability with the aircaft configuration safe life under 90% confidence level it is:

$N_{p,\mathrm{\γ}}=\frac{\[N_{50}\]}{L_f}=\frac{12000.5}{2.56}=4687h$

The foregoing is only presently preferred embodiments of the present invention, not in order to limit the present invention, all essences in the present invention Any amendment, equivalent and the improvement etc. made within god and principle, should be included within the scope of the present invention.

Claims (6)

1. an aircaft configuration safe life based on test and use data fusion of being on active service determines method, it is characterised in that institute State aircaft configuration safe life based on test and use data fusion of being on active service and determine that method includes that homotype aircraft different loads is composed Lower test data fatigue life and the group of planes safe life side of determination when using data obedience logarithm normal distribution fatigue life of being on active service Method, step is:

Step 1, obtains aircaft configuration random censorship data fatigue life: test fatigue life under homotype aircraft different loads spectrum When data and being on active service use that fatigue life, data obeyed logarithm normal distribution, it is believed that consider structure and loading spectrum dispersibility and The aircraft structure fatigue life-span caused also describes by logarithm normal distribution, so flight test vehicle fatigue life under composing with different loads Data use aircraft fatigue lifetime data to directly obtain aircaft configuration random censorship data fatigue life after taking the logarithm with being on active service；

Step 2, calculating aircraft structure fatigue life distribution function parameter: the logarithm normal distribution likelihood under random censorship situation Function and the Maximum-likelihood estimation of lognormal distribution parameter；

Logarithm normal distribution likelihood function under described random censorship situation calculates and concretely comprises the following steps:

If the distribution function of life-span X is F (x, θ) (θ ∈ Θ), density function be f (x, θ), Θ be the non-NULL opener in R, from point Cloth function is in the parent of F (x, θ), randomly draws n individuality, carries out life test；For each individuality, the observation life-span is X_i (i=1 ..., n), correspondingly there is individual truncated time Y_i(i=1 ..., n), observation X that i-th individuality is obtained_i^Y_iTake minimum Value, makes t_i=X_i^Y_i, δ_i=I (X_i＜ Y_i), so can be obtained by data (t_i, δ_i) (i=1 ..., n), δ_i=1 represents t_iIt is Test failure data, δ_i=0 represents t_iIt it is non-failure data；Then data (t₁, δ₁) ..., (t_n, δ_n) likelihood function be:

If N fatigue life of aircraft obeys logarithm normal distribution, then can be designated as

1gN=X～N (μ, σ²)

Distribution function and density function are respectively as follows:

X_i(i=1 ..., r) it is fatigue failure life, X_i(i=r+1 ..., n) it is the tired no-failure life-span；Then likelihood function is:

Step 3, calculates armada Fatigue Life Scatter Factor's and safe life: assume that military service number of aircraft is n frame, tired examination Testing aircraft is 1 frame, and logarithmic fatigue life standard deviation sigma is by being given a large amount of fatigue data statistical results, it is believed that It is known；The random censorship data fatigue life substitution formula that step 1 is obtained:

Above formula is utilized to estimate to obtain the estimated value of logarithmic fatigue life mathematic expectaion μI.e. there is the group of planes aircraft knot of 50% reliability Structure whole life prediction value [N₅₀Isσ is substituted into formula with sample size n sample range+1Computer Group's Fatigue Life Scatter Factor's L_f, further according to aircaft configuration safe life computing formulaCalculate certain reliable Degree and the aircaft configuration safe life N under confidence level_{P, γ}。

2. aircaft configuration safe life based on test and use data fusion of being on active service determines method as claimed in claim 1, It is characterized in that, in described step 2: the specific algorithm of the Maximum-likelihood estimation of lognormal distribution parameter is:

To μ, σ derivation respectively:

OrderEquation below:

3. aircaft configuration safe life based on test and use data fusion of being on active service determines method as claimed in claim 1, It is characterized in that, described aircaft configuration safe life based on test and use data fusion of being on active service determines that method is wrapped further Including homotype aircraft group of planes safe life under same test load is composed and determine method, step is:

Calculate military service CALCULATING STRUCTURAL FATIGUE DAMAGE OF AIRCRAFT value and equivalent pilot time or the number of times that rises and falls；

Obtain aircaft configuration random censorship data fatigue life；

Calculate aircraft structure fatigue life distribution function parameter；

Calculate armada Fatigue Life Scatter Factor's and safe life.

4. aircaft configuration safe life based on test and use data fusion of being on active service determines method as claimed in claim 3, It is characterized in that, described homotype aircraft group of planes safe life under same test load is composed determines that method concretely comprises the following steps:

Step 1, calculates military service CALCULATING STRUCTURAL FATIGUE DAMAGE OF AIRCRAFT value and equivalent pilot time or the number of times that rises and falls: tire out for non-linear fatigue Meter defect theory, the damage measurement formula that n cyclic loading causes is:

S in formula₁For load once maximum in the load series before this load cycle；N₁For corresponding to S₁Fatigue life； n_iFor the cycle-index of i-stage load,D is material constant；Carten and Dolan builds based on fatigue data View: for high strength steel: d=4.8；Other material: d=5.8；

For full machine fatigue test, when testpieces destroys, equivalent damage can be obtained for D₁；It is to say, at test bar D is damaged under part₁Correspond to one fatigue life N₁, then its per pilot time equivalent impairment value is:

Use identical equivalent damage measurement method calculating every frame under practical flight loading spectrum to be on active service and use pilot time N_i's The equivalent impairment value D that aircaft configuration is corresponding_i, then its per pilot time equivalent impairment value is:

Then the conversion factor at equivalent pilot time is:

Utilize military service aircraft practical flight hour be multiplied by conversion factor just obtain this airplane test load compose under equivalent fly Row hourage；

Step 2, acquisition aircaft configuration random censorship data fatigue life: military service aircraft equivalent pilot time number and flight test vehicle Take the logarithm fatigue life later from same distribution, it is believed that be random censorship data fatigue life；

Step 3, calculating aircraft structure fatigue life distribution function parameter: the logarithm normal distribution likelihood under random censorship situation Function and the Maximum-likelihood estimation of lognormal distribution parameter；

Step 4, calculating armada Fatigue Life Scatter Factor's and safe life:

Assuming that military service number of aircraft is n frame, fatigue test aircraft is 1 frame, and logarithmic fatigue life standard deviation sigma is by trying fatigue Test what data statistics result provided, it is believed that be known；Random censorship data fatigue life step 2 obtained substitute into public affairs Formula:

Above formula is utilized to estimate to obtain the estimated value of logarithmic fatigue life mathematic expectaion μThe aircaft configuration i.e. with 50% reliability is tired Labor life estimation value [N₅₀] it isσ is substituted into formula with sample size n sample range+1Computer cluster is tired Factor of life scatter L_f, further according to aircaft configuration safe life computing formulaCalculate certain reliability and confidence Aircaft configuration safe life N under level_{P, γ}。

5. aircaft configuration safe life based on test and use data fusion of being on active service determines method as claimed in claim 4, It is characterized in that, in described step 3: the logarithm normal distribution likelihood function under random censorship situation calculates and concretely comprises the following steps:

If the distribution function of life-span X is F (x, θ) (θ ∈ Θ), density function be f (x, θ), Θ be the non-NULL opener in R, from point Cloth function be F (x, θ) overall in, randomly draw n individual, carry out life test；For each individuality, the observation life-span is X_i (i=1 ..., n), correspondingly there is individual truncated time Y_i(i=1 ..., n), observation X that i-th individuality is obtained by we_i^Y_i Take minima, orderSo can be obtained by data (t_i, δ_i) (i=1 ..., n), δ_i=1 Represent t_iIt is test failure data, δ_i=0 represents t_iIt it is non-failure data；Then data (t₁, δ₁) ..., (t_n, δ_n) likelihood function For:

If N fatigue life of aircraft obeys logarithm normal distribution, then can be designated as

LgN=X～N (μ, σ²)

Distribution function and density function are respectively as follows:

X_i(i=1 ..., r) it is fatigue failure life, X_i(i=r+1 ..., n) it is the tired no-failure life-span；Then likelihood function is:

6. aircaft configuration safe life based on test and use data fusion of being on active service determines method as claimed in claim 4, It is characterized in that, in described step 3: the specific algorithm of the Maximum-likelihood estimation of lognormal distribution parameter is:

To μ, σ derivation respectively:

OrderEquation below: